The height of a triangular road sign is 1 inch shorter than twice its base. if the area of the sign is 60 in.2, which equation could be used to find the base (b) of the sign?

Comment
We should try the very simplest way of finding triangular areas first.

Formula
A = 1/2 b * h

Substitute
Area = 60 in^2
b = x
h = 2x - 1 
60= 1/2 * x * (2x - 1)

Solve
60 = 1/2 * x (2x - 1) Multiply by 2
60 * 2 = x(2x - 1)
120 = x (2x - 1) Remove the brackets.
120 = 2x^2 - x  Subtract 120 from both sides.
2x^2 -  x - 120 = 0 This factors.
(2x + 15)(x - 8) = 0

Solve for x
2x + 15 = 0
2x = - 15
x = -15/2
x = - 7.5 a negative measurement is useless. Discard this answer.

x - 8 = 0
x = 8 

Area (Check)
base = 8
height = 16 - 1 = 15

Area = 1/2 * 8 * 15 = 60 as it should

Answer
Use Area = 1/2 * b * h to find the base and the height.

When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. if you have a multiple-unit rate such as 120 students for every 3 buses, and want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term.